For the function lower f left-parenthesis x right-parenthesis equals negative 4 Start Root x End Root minus 1, find the inverse function.
lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction, x less-than-or-equal-to negative 1
Image with alt text: lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction, x less-than-or-equal-to negative 1
lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction, x greater-than-or-equal-to negative 1
Image with alt text: lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction, x greater-than-or-equal-to negative 1
lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction
Image with alt text: lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction
lower f superscript negative 1 baseline left-parenthesis x right-parenthesis equals Start Fraction left-parenthesis x plus 1 right-parenthesis squared over 16 End Fraction, x less-than-or-equal-to negative 1
The correct answer is:
f^(-1)(x) = (x + 1)^2/16, for x ≤ -1